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who_dares_wins

The maths behind BFT, or why it may benefit some ships more than you think.

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I was bored one day, and decided to follow up on a theory of mine. I've seen many people who only consider how much BFT lowers the reload of their guns when deciding whether or not to take it on their DDs. This leads them to disregard or undervalue BFT on ships with an already low reload time. After doing some maths, I discovered something that seems obvious once explained, but seems to go right over the heads of most people. Counterintuitively, the ships with the lowest base reload time benefit the most from BFT. To explain this, we need to look at BFT differently. Instead of viewing it as a percentage based reload decrease, we should view it as a percentage based rate of fire increase. When you look at it this way, it's quite obvious that the ships with the highest base rate of fire (and therefore lowest base reload) will benefit the most. To help avoid further confusion about this, and to allow you to calculate the usefulness of BFT on a ship yourself, here is a formula for calculating rate of fire increase. To find DPM, simply multiply the answer you get by the shell damage.

 

((60/(Base Reload*0.9))-(60/Base Reload))*Number of guns

 

For your convenience, here is a list of the rate of fire and DPM increases BFT gives to each of the tier X DDs:

 

Gearing: 13.3 rpm, 24000 HE DPM, 28000 AP DPM

Shimakaze:  7.02 rpm, 15087 HE DPM, 15438 AP DPM

Harugumo: 22.2 rpm, 26666 HE DPM,  AP DPM

Z-52: 10 rpm, 15000 HE DPM, 30000 AP DPM

Grozovoi: 10 rpm, 18000 HE DPM, 26000 AP DPM

Khabarovsk: 10.6 rpm, 20266 HE DPM, 27733 AP DPM

Daring: 16 rpm, 27200 HE DPM, 33600 AP DPM

Yueyang: 10 rpm: 18000 HE DPM, 21000 AP DPM

 

Rate of Fire is given to two decimal places and is the total increase provided from all guns. DPM is given to the nearest whole number.

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48 minutes ago, who_dares_wins said:

I was bored one day, and decided to follow up on a theory of mine. I've seen many people who only consider how much BFT lowers the reload of their guns when deciding whether or not to take it on their DDs. This leads them to disregard or undervalue BFT on ships with an already low reload time. After doing some maths, I discovered something that seems obvious once explained, but seems to go right over the heads of most people. Counterintuitively, the ships with the lowest base reload time benefit the most from BFT. To explain this, we need to look at BFT differently. Instead of viewing it as a percentage based reload decrease, we should view it as a percentage based rate of fire increase. When you look at it this way, it's quite obvious that the ships with the highest base rate of fire (and therefore lowest base reload) will benefit the most. To help avoid further confusion about this, and to allow you to calculate the usefulness of BFT on a ship yourself, here is a formula for calculating rate of fire increase. To find DPM, simply multiply the answer you get by the shell damage.

 

((60/(Base Reload*0.9))-(60/Base Reload))*Number of guns

 

For your convenience, here is a list of the rate of fire and DPM increases BFT gives to each of the tier X DDs:

 

Gearing: 13.3 rpm, 24000 HE DPM, 28000 AP DPM

Shimakaze:  7.02 rpm, 15087 HE DPM, 15438 AP DPM

Harugumo: 22.2 rpm, 26666 HE DPM,  AP DPM

Z-52: 10 rpm, 15000 HE DPM, 30000 AP DPM

Grozovoi: 10 rpm, 18000 HE DPM, 26000 AP DPM

Khabarovsk: 10.6 rpm, 20266 HE DPM, 27733 AP DPM

Daring: 16 rpm, 27200 HE DPM, 33600 AP DPM

Yueyang: 10 rpm: 18000 HE DPM, 21000 AP DPM

 

Rate of Fire is given to two decimal places and is the total increase provided from all guns. DPM is given to the nearest whole number.

You're making the same mistake that is done by people who say "rate of fire is already good, no need for BFT" - you're too focused on rate of fire. What counts is the DPM and how important it is for the ship (and player, since a lot depends on playstyle too) in question - and we're talking about the importance of DPM (rather than raw values) for a reason: the numbers can be misleading due to hull and ballistic differences - Khaba is a much more dangerous gunboat than the DPM calculation alone might imply.

 

To put it simply:

If you find yourself often trying to melt down targets by firing continuously to get what you can out of your DPM - BFT is going to help you by providing a nice +11% DPM. If you rarely use your guns and/or rarely keep them blazing for long - then you probably won't see much benefit.

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53 minutes ago, who_dares_wins said:

Instead of viewing it as a percentage based reload decrease, we should view it as a percentage based rate of fire increase

RoF and DPM will be directly correlated, and DPM is a much better value to look at

 

10% reload length decrease will be 11.(1)% DPM increase no matter what you started with, so all ships gain the same %. What differs is that the bigger base value you have, the bigger that same % raw value is for you

 

 

Examples:

 

5s reload 120 k DPM -> 4.5s reload 133.(3) k DPM.

5 * 0.9 = 4.5

120 * 1.11(1) = 133.(3)

 

10s reload 90 k DPM -> 9s reload 100k DPM

10 * 0.9 = 9

90 * 1.11(1) = 100

 

^ in both cases it's the same 0.9 & 1.11(1), so the bonus on 1st is larger only bcuz base on 1st is larger

 

 

Also what eliastion said

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Two more important considerations than dpm/rof to look at: 

 

- Durations of engagements: if lower than 10x reload time (25s for fastest, Daring) then BFT doesnt matter at all since you will not be able to squeeze in another volley

-  uptime of gun usage during a match (khabarovsk shoots on cooldown for 20 mins, shima doesnt)

 

also what Elastion said.

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1 hour ago, GulvkluderGuld said:

- Durations of engagements: if lower than 10x reload time (25s for fastest, Daring) then BFT doesnt matter at all since you will not be able to squeeze in another volley

 

Not necessarily. When DD-hunting in Kitakaze or Daring, the enemy is likely to try and run away. The first couple salvoes are the most effective and then the effectiveness drops off as the enemy starts reacting to the threat you pose. Being a little bit faster can still give a slight bump to that initial effectiveness, even if not enough time has yet passed to grant you the extra shot.

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Question is:

are those 3 points worth that tiny bit of DPM or wouldnt they better invested in something else?

 

SE gives you 3500 more HP at tier10, that 1-2 salvos from a DD you can survive more. Superintendend gives you one extra of every consumable. For example for the Grozovoi thats 1 extra healing and 1 extra smoke, well, plus all those others, but those two can indirectly buff the damage you do by keeping you alive.

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On 12/8/2018 at 8:35 PM, Seeigel said:

Question is:

are those 3 points worth that tiny bit of DPM or wouldnt they better invested in something else?

 

SE gives you 3500 more HP at tier10, that 1-2 salvos from a DD you can survive more. Superintendend gives you one extra of every consumable. For example for the Grozovoi thats 1 extra healing and 1 extra smoke, well, plus all those others, but those two can indirectly buff the damage you do by keeping you alive.

It depends heavily on DD in question and playstyle. Grozovoi for example is one DD that really benefits from SI, SE and BFT, to the point that some run it without CE and LS just to get all three. Meanwhile on most DDs, SI is just another smoke and another speed boost. Something like Chung Mu (and old YY) meanwhile would only get a smoke/radar (while having already plenty smokes) and a speed boost, making BFT much better to boost the already good dpm. There you can take it ontop of SE and either TAE or RPF, whichever fits your playstyle more. On IJN DDs meanwhile, BFT is one of the least taken skills, because you hardly ever want to be in a straight up fair gunfight and RPF helps avoid them, TAE is your main dpm increase and SE is better to survive not just DDs, but also survive other sources of damage. In general, SE often is a better skill, as extra hp are more useful than extra dpm, but I'd think usually you'd want both, not BFT instead of SE. BFT's opportunity cost should be viewed more vs SI, TAE or a second 4 point skill.

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On 12/8/2018 at 7:35 PM, Seeigel said:

Question is:

are those 3 points worth that tiny bit of DPM or wouldnt they better invested in something else?

 

SE gives you 3500 more HP at tier10, that 1-2 salvos from a DD you can survive more. Superintendend gives you one extra of every consumable. For example for the Grozovoi thats 1 extra healing and 1 extra smoke, well, plus all those others, but those two can indirectly buff the damage you do by keeping you alive.

Completely this, BFT is a luxury skill. 

 

For DDs atleast SE must be the first 3rd level pick. As you can quote all the DPM buffs you like but a ship with 0 HP also has 0 DPM. And yeah SI is decent with heals, smokes, reload boosters etc.

 

I do have BFT on some of my ships but it's usually the last pick. AR is better than BFT as the buffs include Torps and it encourages you to attack!!

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